Statics-Two wires holding traffic light

In summary, the conversation involves finding the tension in two wires supporting a traffic light with a mass of 33kg, given the angles of the wires and the equation for tension. Through calculations, it is determined that the left wire has 230N of tension and the right wire has 180N of tension.
  • #1
4
0
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I don't know what i did wrong

Find the tension in the two wires supporting the traffic light
Mass of light= 33 kg
θ of FT1= 53°
θ of FT2=37°

Ʃfx=0
Ft1cos53-ft2cos37=0
ft1cos53=ft2cos37

Ʃfy=mg
ft1sin53-ft2sin37=mg
ft1sin53=mg+ft2sin37
ft1=(ft2sin37+mg)/sin53
ft1=1.33ft2

1.33ft2=(ft2sin37+mg)/sin53
1.33ft2=.72ft2+mg
.61ft2=323.73 N
Ft2=530.7n

ft1cos53=ft2cos37
ft1cos53=423.84n
ft1=704.26n
 
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  • #2
Tension forces always pull away from the objects on which they act. In the horizontal direction, your equation is correct. Not so in the vertical direction.
 
  • #3
This is what I got:
TLsin(53o) + TRsin(37o) - 294 N= 0 TRcos(37o) - TLcos(53o) = 0
TR = TLcos(53o)/cos(37o)

TLsin(53o) + TRsin(37o) - 294N= 0
TLsin(53o) + {TLcos(53o)/cos(37o)}sin(37o) - 294 = 0
TLsin(53o) + TLcos(53o)tan(37o) = 294N
TL(sin(53o) + cos(53o)tan(37o)) = 294N
TL = (294 N)/(sin(53o) + cos(53o)tan(37o)) = 234.79884N = 230N

TR = TLcos(53o)/cos(37o)
TR = (234.79884 N)cos(53o)/cos(37o) = 176.9336 N = 180N

Left wire has 230N of tension
Right wire has 180N of tension
 
  • #4
I don't know where you got the 294N from? 33kg * 9.8 = 323N. g is 9.8, not 8.9!

Your maths seems right though.

You can check your answer easily also. 230sin(53) + 180sin(37) = 292N, which is close enough (since you rounded your answers) to 294.
 
  • #5
Well dangit... I guess I got that one wrong then!
 
  • #6
PhantomJay is correct

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Hope this helps.
 

What is statics and how does it apply to two wires holding traffic lights?

Statics is a branch of mechanics that deals with the study of objects at rest or in equilibrium. It is used to analyze and predict the behavior of structures and objects under various forces. In the case of two wires holding a traffic light, statics is used to determine the tension and forces exerted on the wires to keep the traffic light in place.

How are the wires able to hold the weight of the traffic light?

The wires holding a traffic light are able to hold its weight due to the principle of tension. Tension is the force that is transmitted through a wire, rope, or cable when it is pulled tight by forces acting from opposite ends. In this case, the wires are under tension, and the balanced forces acting on them keep the traffic light in place.

What factors influence the tension in the wires holding the traffic light?

The tension in the wires holding a traffic light is influenced by several factors, including the weight of the traffic light, the distance between the wires, the angle at which the wires are attached to the traffic light, and the material and thickness of the wires.

Can the tension in the wires change over time?

Yes, the tension in the wires holding a traffic light can change over time. Factors such as weather conditions, vibrations, and the weight of the traffic light itself can affect the tension in the wires. It is important to regularly inspect and maintain the wires to ensure they can continue to hold the traffic light securely.

What can happen if the tension in one of the wires is significantly different from the other?

If the tension in one of the wires holding a traffic light is significantly different from the other, it can cause the traffic light to become unbalanced and potentially fall. This can also put added stress on the remaining wire, potentially causing it to fail as well. It is important to maintain equal tension in both wires to ensure the stability and safety of the traffic light.

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